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Stability and boundedness results for solutions of certain third order nonlinear vector differential equations. (English) Zbl 1132.34328

Consider the nonlinear vector differential equation

$\stackrel{⃛}{x}+F\left(x,\stackrel{˙}{x},\stackrel{¨}{x}\right)\stackrel{¨}{x}+B\left(t\right)\stackrel{˙}{x}+h\left(\stackrel{˙}{x}\right)=p\left(t,x,\stackrel{˙}{x},\stackrel{¨}{x}\right),\phantom{\rule{1.em}{0ex}}t\ge 0,\phantom{\rule{2.em}{0ex}}\left(*\right)$

where $F$ and $B$ are symmetric $n×n$-matrices depending continuously on their arguments, the functions $h$ and $p$ mapping into ${ℝ}^{n}$ are also continuous functions. Using Lyapunov’s direct method, the authors present conditions guaranteeing the asymptotic stability of the zero solution of (*) and the boundedness of all solutions.

##### MSC:
 34D20 Stability of ODE 34C11 Qualitative theory of solutions of ODE: growth, boundedness
##### References:
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